Beispiel #1
0
def __solve_nodal_circuit_sparse(Ac, Yb, E):
    '''
	Based on Chua, 1975
	Solve circuit based on nodal  analysis\n
	Ac: nodal incidence matrix (with reference node)\n
	Yb: branch admitance matrix\n
	E: branch source vector
	'''
    if isinstance(Ac, csr_matrix) and isinstance(
            Yb, csr_matrix) and isinstance(E, csr_matrix):
        A = matrix_aux.delete_sparse_mask(Ac, [0], 0)
        del (Ac)
        At = csr_matrix.transpose(A)
        Yn = A.dot(Yb).dot(At)
        Jn = -A.dot(Yb).dot(E)
        del (A)
        vn = spsolve(Yn, Jn)
        del (Yn)
        del (Jn)
        vn = vn.T
        v_b = At.dot(vn)
        #		v_b=csr_matrix.dot(At,vn)
        v = (v_b + E.T).T
        i = Yb.dot(v)
    return i
Beispiel #2
0
def __solve_nodal_circuit_sparse(Ac,Yb,E):
	'''
	Based on Chua, 1975
	Solve circuit based on nodal  analysis\n
	Ac: nodal incidence matrix (with reference node)\n
	Yb: branch admitance matrix\n
	E: branch source vector
	'''
	if isinstance(Ac,csr_matrix) and isinstance(Yb,csr_matrix) and isinstance(E,csr_matrix):
		A=matrix_aux.delete_sparse_mask(Ac,[0],0)
		At=csr_matrix.transpose(A)
		Yn=A.dot(Yb).dot(At)
#		Yn=(A*Yb)*At
		Jn=-A.dot(Yb).dot(E)
#		Jn=-csr_matrix.dot(csr_matrix.dot(A,Yb),E)
		vn=spsolve(Yn, Jn)
		vn=vn.T
		v_b=At.dot(vn)
#		v_b=csr_matrix.dot(At,vn)
		v=(v_b+E.T).T
		i=Yb.dot(v)
	return i
def integration_process(folder_path, preProcData):
    file_names = File_names()
    results_folder = file_names.get_results_folder_name()
    results_path = os.path.join(folder_path, results_folder)

    #	Source field
    run_surface_integral = False
    run_biot_savart = True
    run_VS = False

    #%% Instances and geral definitions
    global_variables = GlobalVariables()
    error = Errors()
    operations = Operations()
    materials_lib = get_materials_lib()
    vacuum = Vacuum()
    get_gauss_points_class = GaussPoints()
    shape_functions = ShapeFuncions()
    operations = Operations()

    str_noflux_face = global_variables.str_noflux_face
    results_folder = file_names.get_results_folder_name()

    face = Face()
    #------------------------------------------------------------------------------
    # Setup
    regions_material = preProcData.RegionMaterial
    regions_excitation = preProcData.RegionExcitation
    boundary = preProcData.BC
    external_reluctances = preProcData.ExternalReluctances
    coupling = preProcData.CoupNet

    #------------------------------------------------------------------------------
    # Mesh
    mesh_data = preProcData.MeshData
    all_elem_nodes_3D = mesh_data.ElemNodes
    nodes_coordenates = mesh_data.NodesCoordenates
    elem_tags = mesh_data.ElemTags
    elem_type = mesh_data.ElemType

    #%% Get 2D and 3D elements, with their materials name
    elem_2D_ID = list()
    elem_type_3D = list()
    elem_nodes_3D = list()
    elem_tags_3D = list()
    region_ID_list_3D = list()
    number_elements_2D = 0

    for counter, each_elem in enumerate(all_elem_nodes_3D):
        this_elem_type = elem_type[counter]
        if this_elem_type < 4:
            elem_2D_ID.append(counter)
            number_elements_2D += 1
        else:
            elem_nodes_3D.append(each_elem)
            elem_type_3D.append(elem_type[counter])
            elem_tags_3D.append(elem_tags[counter])

            find = False
            for each_region in regions_material:
                if each_region.RegionNumber == elem_tags[counter][0]:
                    region_ID_list_3D.append(each_region.MaterialName)
                    find = True
            if not find:
                error.physical_surface_not_defined(
                    str(each_region.RegionNumber), elem_tags[counter][0])

    number_elements = len(elem_nodes_3D)
    number_nodes = len(nodes_coordenates)
    faces_ID = list()
    faces_list = list()
    plot_test_coord = list()
    plot_test_field = list()

    #%%Get source field
    field_solution = list()
    run_permanent_magnets = False

    #	Run Permanent Magnets
    for each_region in regions_material:
        for each in materials_lib[each_region.MaterialName].Hc:
            if each != 0.0:
                permanent_magnets.run_permanent_magnets(
                    preProcData, folder_path)
                run_permanent_magnets = True
                break

    #Read the fields
    if run_biot_savart or run_permanent_magnets:

        results_folder = file_names.get_results_folder_name()
        folder_name = os.path.join(folder_path, results_folder)

        #Gauss points IDs
        this_file_name = file_names.get_Gauss_points_ID_file_name()
        full_path = os.path.join(folder_name, this_file_name)
        points_IDs = np.genfromtxt(full_path,
                                   delimiter=' ',
                                   dtype='int',
                                   usecols=(1, 2, 3, 4))
        points_ID_elem_all = np.genfromtxt(full_path,
                                           delimiter=' ',
                                           dtype='int',
                                           usecols=(0))
        points_ID_elem = points_ID_elem_all - number_elements_2D
        points_ID_elem = points_ID_elem.tolist()
        points_ID_elem_all = points_ID_elem_all.tolist()

        #		Gauss points coordinates
        this_file_name = file_names.get_Gauss_points_coordinates_file_name()
        full_path = os.path.join(folder_name, this_file_name)
        coordinates = np.genfromtxt(full_path, delimiter=' ', dtype='double')

        #		Fields
        this_file_name = file_names.get_Gauss_points_H_field_file_name()
        #		this_file_name="H_source_FFEM.txt"

        full_path = os.path.join(folder_name, this_file_name)
        fields = np.genfromtxt(full_path, delimiter=' ', dtype='double')

        for elem_counter in range(0, number_elements):
            this_elem_type = elem_type_3D[elem_counter]
            gauss_points = get_gauss_points_class.get_gauss_points(
                this_elem_type)
            number_integ_points = len(
                get_gauss_points_class.get_gauss_points(this_elem_type))
            this_points_field = list()

            if elem_counter in points_ID_elem:

                this_elem = points_ID_elem.index(elem_counter)
                for k in points_IDs[this_elem].tolist():
                    Hxy = np.zeros((3, 1))
                    Hxy[0, 0] = fields[k, 0]
                    Hxy[1, 0] = fields[k, 1]
                    Hxy[2, 0] = fields[k, 2]
                    this_points_field.append(Hxy)

            else:
                for k in xrange(number_integ_points):
                    Hxy = np.zeros((3, 1))
                    this_points_field.append(Hxy)
            field_solution.append(this_points_field)

    run_external_circuit = False
    if len(coupling) > 0:
        run_external_circuit = True

#%%Creates the face list
    print_message("Creating faces list")
    for elem_counter in range(0, number_elements):
        number_local_faces = shape_functions.get_number_faces(this_elem_type)
        this_elem_type = elem_type_3D[elem_counter]
        this_element_nodes = elem_nodes_3D[elem_counter]
        faces_nodes_ID = shape_functions.get_nodes_ID_2_face(this_elem_type)
        number_faces, nodes_per_face = faces_nodes_ID.shape
        local_faces_ID = list()
        for local_face_counter in range(0, number_faces):
            nodes_list = list()
            for node_counter in range(nodes_per_face):
                node_ID = faces_nodes_ID[local_face_counter, node_counter]
                nodes_list.append(this_element_nodes[node_ID])
            local_faces_ID.append(
                face.add_to_list(nodes_list, elem_counter, faces_list))
        faces_ID.append(local_faces_ID)
    print_message("Creating faces list - Done")

    #%%Integration
    print_message("Integration process")

    num_meshed_rel = len(faces_list)
    num_non_meshed_rel = len(external_reluctances)
    num_total_rel = num_meshed_rel + num_non_meshed_rel

    #sparse matrix
    cols_rel_sparse = list()
    rows_rel_sparse = list()

    #reluctance matrix
    diagonal = list()
    for each_element_faces in faces_ID:
        numbre_faces_this_element = len(each_element_faces)
        for face_counter_1 in xrange(numbre_faces_this_element):
            pos_1 = each_element_faces[face_counter_1]
            for face_counter_2 in xrange(numbre_faces_this_element):
                pos_2 = each_element_faces[face_counter_2]
                if pos_1 == pos_2:
                    if pos_1 not in diagonal:
                        rows_rel_sparse.append(pos_1)
                        cols_rel_sparse.append(pos_2)
                        diagonal.append(pos_1)
                else:
                    rows_rel_sparse.append(pos_1)
                    cols_rel_sparse.append(pos_2)

    data_rel_sparse = np.zeros(len(rows_rel_sparse))
    faces_rel_spare = csr_matrix(
        (data_rel_sparse, (rows_rel_sparse, cols_rel_sparse)),
        shape=(num_total_rel, num_total_rel))

    #fmm matrix
    cols_fmm_sparse = np.zeros(num_meshed_rel)
    rows_fmm_sparse = xrange(0, num_meshed_rel)
    data_fmm_sparse = np.zeros(num_meshed_rel)
    fmm_sparse = csr_matrix(
        (data_fmm_sparse, (rows_fmm_sparse, cols_fmm_sparse)),
        shape=(num_total_rel, 1))

    #source_flux matrix
    cols_source_flux_sparse = np.zeros(num_meshed_rel)
    rows_source_flux_sparse = xrange(0, num_meshed_rel)
    data_source_flux_sparse = np.zeros(num_meshed_rel)
    source_flux_sparse = csr_matrix(
        (data_source_flux_sparse,
         (rows_source_flux_sparse, cols_source_flux_sparse)),
        shape=(num_total_rel, 1))
    #grad_phi matrix
    #	cols_grad_phi_sparse=np.zeros(num_meshed_rel)
    #	rows_grad_phi_sparse=xrange(0,num_meshed_rel)
    #	data_grad_phi_sparse=np.zeros(num_meshed_rel)
    #	grad_phi_sparse=csr_matrix((data_grad_phi_sparse, (rows_grad_phi_sparse, cols_grad_phi_sparse)), shape=(num_total_rel,1))

    this_elem_type = ""
    plot_field = list()
    plot_shape_functions = list()
    #	plot_test_coord=list()
    BC_nodes = list()
    BC_values = list()

    for elem_counter in xrange(number_elements):
        this_elem_type_changed = elem_type_3D[elem_counter]
        if this_elem_type != this_elem_type_changed:
            this_elem_type = this_elem_type_changed
            gauss_points = get_gauss_points_class.get_gauss_points(
                this_elem_type)
            number_local_faces = shape_functions.get_number_faces(
                this_elem_type)
            number_integ_points = len(
                get_gauss_points_class.get_gauss_points(this_elem_type))
            wtri = get_gauss_points_class.get_integration_weight(
                this_elem_type)

        faces_ID_Elem = faces_ID[elem_counter]
        this_element_nodes = elem_nodes_3D[elem_counter]
        mur_r = materials_lib[region_ID_list_3D[elem_counter]].Permeability
        mu_elem = vacuum.mu0 * mur_r
        #		x=nodes_coordenates[this_element_nodes[0]][1]

        # Get W at reference element
        w_local_this_element = list()  #[gauss point][face]
        for each_integ_point in xrange(number_integ_points):

            #u,v,w coordinates
            u = gauss_points[each_integ_point, 0]
            v = gauss_points[each_integ_point, 1]
            w = gauss_points[each_integ_point, 2]

            # Shape functions @ reference element
            w_local_this_point = shape_functions.get_facet_shape_function(
                this_elem_type, u, v, w)
            w_local_this_element.append(w_local_this_point)

# Shape functions @ real element for each face
        w_real_all_points = list(
        )  # w_real_lista[0] contains  the shape function of all points for face 0

        #Boundary conditions
        #		Hxy=field_solution[elem_counter][each_integ_point]
        #		if Hxy[0,0]!=0 or Hxy[1,0]!=0 or Hxy[2,0]!=0:
        #			BC_nodes.append(elem_counter)
        #			BC_values.append(x)

        #   Face 0...Fn
        #P0  W
        #Pn

        for face_counter in xrange(number_local_faces):
            w_real_this_point = list()
            for point_counter in range(0, number_integ_points):
                w_local = w_local_this_element[point_counter][face_counter]
                w_real = operations.convert_local_real_Piola(
                    this_elem_type, w_local[0, 0], w_local[0, 1],
                    w_local[0, 2], this_element_nodes, nodes_coordenates)
                w_real_this_point.append(w_real)
            w_real_all_points.append(w_real_this_point)

# Source fields
        for local_face_counter in xrange(number_local_faces):

            w_1 = copy.deepcopy(w_real_all_points[local_face_counter])
            face_ID_1 = faces_ID_Elem[local_face_counter]

            if faces_list[face_ID_1].elem_2 == elem_counter:
                for each in w_1:
                    each = matrix_aux.invert_w(each)

            elem_ID_all = elem_counter + number_elements_2D

            #			this_3D_ID=points_ID_elem_all.index(elem_ID_all)
            # mmf source integration process
            source = 0
            this_face_nodes = faces_list[face_ID_1].nodes_list
            #
            #
            this_elem = points_ID_elem.index(elem_counter)
            this_gauss_points_ID = points_IDs[this_elem].tolist()

            Hxy = np.zeros((3, 1))
            for each_integ_point in xrange(number_integ_points):
                if run_biot_savart or run_permanent_magnets:
                    #					Hxy=field_solution[elem_counter][each_integ_point]
                    this_point_ID = this_gauss_points_ID[each_integ_point]
                    Hxy[0, 0] = fields[this_point_ID, 0]
                    Hxy[1, 0] = fields[this_point_ID, 1]
                    Hxy[2, 0] = fields[this_point_ID, 2]

                    if Hxy[0, 0] != 0 or Hxy[1, 0] != 0 or Hxy[2, 0] != 0:

                        w_1_this_point = w_1[each_integ_point]

                        #u,v,p coordinates
                        u = gauss_points[each_integ_point, 0]
                        v = gauss_points[each_integ_point, 1]
                        p = gauss_points[each_integ_point, 2]
                        w = w_1_this_point

                        plot_shape_functions.append(w)

                        plot_test_field.append(Hxy)
                        plot_test_coord.append(coordinates[this_point_ID])
                        # Jacobian
                        jac = operations.get_jacobian(this_elem_type,
                                                      this_element_nodes,
                                                      nodes_coordenates, u, v,
                                                      p)
                        det_jac = np.linalg.det(jac)
                        abs_det_jac = np.abs(det_jac)
                        #Integration
                        source = source + wtri * abs_det_jac * matrix_aux.dot_product(
                            w, Hxy)

            fmm_sparse[face_ID_1, 0] = fmm_sparse[face_ID_1, 0] + source

            # Relutances integration process
            for local_face_counter_2 in xrange(number_local_faces):
                w_2 = copy.deepcopy(w_real_all_points[local_face_counter_2])
                face_ID_2 = faces_ID_Elem[local_face_counter_2]

                if faces_list[face_ID_2].elem_2 == elem_counter:
                    for each in w_2:
                        each = matrix_aux.invert_w(each)

                wtot = 0.0
                for each_integ_point in range(0, number_integ_points):
                    u = gauss_points[each_integ_point, 0]
                    v = gauss_points[each_integ_point, 1]
                    p = gauss_points[each_integ_point, 2]

                    # Jacobian
                    jac = operations.get_jacobian(this_elem_type,
                                                  this_element_nodes,
                                                  nodes_coordenates, u, v, p)
                    det_jac = np.linalg.det(jac)
                    abs_det_jac = np.abs(det_jac)

                    # Reluctance
                    w_1_this_point = w_1[each_integ_point]
                    w_2_this_point = w_2[each_integ_point]
                    wtot = wtot + wtri * abs_det_jac * matrix_aux.dot_product(
                        w_1_this_point, w_2_this_point) / mu_elem

                faces_rel_spare[face_ID_1, face_ID_2] += wtot
    print_message("Integration process - Done")

    #%% Connection between the physical line with the circuit node
    print_message("External faces")

    for counter, each_face in enumerate(faces_list):
        if each_face.elem_2 == str_noflux_face:
            for each_face_con in elem_2D_ID:
                nodes_face_shared = all_elem_nodes_3D[each_face_con]
                phys_line = elem_tags[each_face_con][0]

                #Coupling with external reluctances
                for each_coupling in coupling:
                    if each_coupling.PhysLine == phys_line:

                        bool_connect = True
                        for each_node_this_face in each_face.nodes_list:
                            if each_node_this_face not in nodes_face_shared:
                                bool_connect = False

                        if bool_connect:
                            # Redefine the face
                            new_face = Face(
                                each_face.nodes_list, each_face.elem_1,
                                each_coupling.Node + number_elements)
                            faces_list[counter] = new_face
                            each_coupling.Face_ID_List.append(counter)

#%% Insert the flux sources
#	BC_nodes=list()
    if run_surface_integral:
        folder_name = os.path.join(folder_path, results_folder)
        full_path = os.path.join(folder_name, "flux_surface.txt")
        flux_data = np.genfromtxt(full_path, delimiter=' ', dtype='double')
        flux_source = flux_data[:, 1]
        flux_source_elem_ID = flux_data[:, 0]
        num_faces_surface_integral = len(flux_source_elem_ID)
        external_node_surface_ID_counter = 0

        for face_counter in xrange(num_faces_surface_integral):
            this_elem_face_ID = int(flux_source_elem_ID[face_counter])
            this_face_nodes_elem = set(all_elem_nodes_3D[this_elem_face_ID])

            for counter, each_face in enumerate(faces_list):
                this_face_nodes = set(each_face.nodes_list)
                if this_face_nodes_elem.issubset(this_face_nodes):
                    #					print this_elem_face_ID
                    #					external_node_surface_ID=len(coupling)+number_elements-1
                    #					BC_nodes.append(external_node_surface_ID)
                    #					external_node_surface_ID_counter+=1
                    new_face = Face(each_face.nodes_list, each_face.elem_1,
                                    each_face.elem_2)
                    faces_list[counter] = new_face
                    source_flux_sparse[counter] = flux_source[face_counter]
                    faces_rel_spare[counter, counter] = 10000000000000000.0
                    fmm_sparse[counter, 0] = 0.0
#					print each_face.elem_1
#					break

#	BC_values=[0]*len(BC_nodes)

#%% Delete the faces without external connections
    faces_ID_deleted_list = list()
    faces_deleted_list = list()

    #Delete from reluctances and fmm matrix
    counter = 0
    for face_counter in xrange(len(faces_list)):
        if faces_list[face_counter].elem_2 == str_noflux_face:
            faces_ID_deleted_list.append(face_counter)

    faces_rel_spare = matrix_aux.delete_sparse_mask(faces_rel_spare,
                                                    faces_ID_deleted_list, 0)
    faces_rel_spare = matrix_aux.delete_sparse_mask(faces_rel_spare,
                                                    faces_ID_deleted_list, 1)
    fmm_sparse = matrix_aux.delete_sparse_mask(fmm_sparse,
                                               faces_ID_deleted_list, 0)
    source_flux_sparse = matrix_aux.delete_sparse_mask(source_flux_sparse,
                                                       faces_ID_deleted_list,
                                                       0)

    ##Delete from faces_list
    counter = 0
    for each in faces_ID_deleted_list:
        face_ID = each + counter
        this_face = faces_list[face_ID]
        faces_list.remove(this_face)
        faces_deleted_list.append(this_face)
        counter -= 1

#%% Add the external circuit reluctances
    number_deleted = len(faces_deleted_list)
    for counter in xrange(num_non_meshed_rel):

        #reluctance value
        material = external_reluctances[counter].Material
        mur = materials_lib[material].Permeability
        LS = external_reluctances[counter].LS
        mu_elem = vacuum.mu0 * mur
        reluctance_value = LS / mu_elem

        this_position = num_meshed_rel - number_deleted + counter
        faces_rel_spare[this_position, this_position] = reluctance_value
        fmm_sparse[this_position] = external_reluctances[counter].fmm
        source_flux_sparse[this_position] = external_reluctances[counter].flux

    external_nodes_list = list()

    for each in external_reluctances:

        #Get the list of external nodes
        if each.node_from not in external_nodes_list:
            external_nodes_list.append(each.node_from)
        if each.node_to not in external_nodes_list:
            external_nodes_list.append(each.node_to)

#create a new face in the faces_list
        new_face = Face([], each.node_from + number_elements,
                        each.node_to + number_elements)
        faces_list.append(new_face)

#Get the list of external nodes
    for each in coupling:
        if each.Node not in external_nodes_list:
            external_nodes_list.append(each.Node)

    print_message("External faces - Done")

    #%% Incidence matrix
    print_message("Incidence matrix")
    external_nodes = 0

    if run_external_circuit:
        external_nodes += len(external_nodes_list)
#	elif run_surface_integral:
#		external_nodes+=len(BC_nodes)
    else:
        external_nodes += 0

    number_faces_list = len(faces_list)
    total_nodes = number_elements + external_nodes

    rows_incidence_sparse = list()
    cols_incidence_sparse = list()
    data_incidence_sparse = list()

    for counter in xrange(number_faces_list):
        this_face = faces_list[counter]
        rows_incidence_sparse.append(this_face.elem_1)
        cols_incidence_sparse.append(counter)
        data_incidence_sparse.append(1.0)

        rows_incidence_sparse.append(this_face.elem_2)
        cols_incidence_sparse.append(counter)
        data_incidence_sparse.append(-1.0)

    incidence_matrix_sparse = csr_matrix(
        (data_incidence_sparse,
         (rows_incidence_sparse, cols_incidence_sparse)),
        shape=(total_nodes, number_faces_list))

    print_message("Incidence matrix - Done")

    #%%Plot test fields
    Gmsh_file_name = "test_H_field.txt"
    path = os.path.join(results_path, Gmsh_file_name)
    Create_Vector_field(plot_test_coord, plot_test_field, path, "H test")

    Gmsh_file_name = "test_W.txt"
    path = os.path.join(results_path, Gmsh_file_name)
    Create_Vector_field(plot_test_coord, plot_shape_functions, path,
                        "Shape function")

    print_message("Saving matrices")
    np.save(os.path.join(results_path, "faces_rel_spare_algo"),
            faces_rel_spare.toarray())
    np.save(os.path.join(results_path, "fmm_sparse_algol"),
            fmm_sparse.toarray())
    np.save(os.path.join(results_path, "incidence_matrix_algo"),
            incidence_matrix_sparse.toarray())
    print_message("Saving matrices: Done")

    return faces_rel_spare, incidence_matrix_sparse, fmm_sparse, source_flux_sparse, faces_ID, results_path, faces_ID_deleted_list, faces_list, faces_deleted_list, BC_nodes, BC_values
def integration_process(folder_path,preProcData):
	file_names=File_names()
	results_folder=file_names.get_results_folder_name()
	results_path=os.path.join(folder_path,results_folder)

#	Source field
	mu0=4.0*math.pi*math.pow(10.0,-7.0)
	run_surface_integral=True
	run_biot_savart=True
	run_VS=False
	perf_mag_surf=177
	one_layer_ID=175
#%% Instances and geral definitions
	global_variables=GlobalVariables()
	error=Errors()
	operations=Operations()
	materials_lib=get_materials_lib()
	vacuum=Vacuum()
	get_gauss_points_class=GaussPoints()
	shape_functions=ShapeFuncions()
	operations=Operations()

	str_noflux_face=global_variables.str_noflux_face
	results_folder=file_names.get_results_folder_name()

	face=Face()
	#------------------------------------------------------------------------------
	# Setup
	regions_material=preProcData.RegionMaterial
	regions_excitation=preProcData.RegionExcitation
	boundary=preProcData.BC
	external_reluctances=preProcData.ExternalReluctances
	coupling=preProcData.CoupNet


	#------------------------------------------------------------------------------
	# Mesh
	mesh_data=preProcData.MeshData
	all_elem_nodes_3D= mesh_data.ElemNodes
	nodes_coordenates=mesh_data.NodesCoordenates
	elem_tags=mesh_data.ElemTags
	elem_type=mesh_data.ElemType

	#%% Get 2D and 3D elements, with their materials name
	elem_2D_ID=list()
	elem_type_3D=list()
	elem_nodes_3D=list()
	elem_tags_3D=list()
	region_ID_list_3D=list()
	number_elements_2D=0
	nodes_phys_surf=list()

	for counter,each_elem in enumerate(all_elem_nodes_3D):
		this_elem_type=elem_type[counter]
		if this_elem_type<4:
			elem_2D_ID.append(counter)
			number_elements_2D+=1
			if elem_tags[counter][0]==perf_mag_surf:
				for each in all_elem_nodes_3D[counter]:
					if each not in nodes_phys_surf:
						nodes_phys_surf.append(each)
		else:
			elem_nodes_3D.append(each_elem)
			elem_type_3D.append(elem_type[counter])
			elem_tags_3D.append(elem_tags[counter])

			find=False
			for each_region in regions_material:
				if each_region.RegionNumber==elem_tags[counter][0]:
					region_ID_list_3D.append(each_region.MaterialName)
					find=True
			if not find:
			   error.physical_surface_not_defined(str(each_region.RegionNumber),elem_tags[counter][0])

	number_elements=len(elem_nodes_3D) #only 3D elements
	number_nodes=len(nodes_coordenates)
	faces_ID=list()
	faces_list=list()
#	nodes_phys_surf=set(nodes_phys_surf)
	plot_field=list()
	plot_shape_functions=list()
	plot_test_coord=list()



	#%%Get source field
	field_solution=list()
	run_permanent_magnets=False

#	Run Permanent Magnets
	for each_region in regions_material:
		for each in materials_lib[each_region.MaterialName].Hc:
			if each !=0.0:
				permanent_magnets.run_permanent_magnets(preProcData,folder_path)
				run_permanent_magnets=True
				break

	#Read the fields
	if run_biot_savart or run_permanent_magnets:

		results_folder=file_names.get_results_folder_name()
		folder_name=os.path.join(folder_path,results_folder)

		#Gauss points IDs
		this_file_name=file_names.get_Gauss_points_ID_file_name()
		full_path=os.path.join(folder_name,this_file_name)
		points_IDs = np.genfromtxt(full_path,delimiter=' ',dtype='int', usecols=(1,2,3,4))
		points_ID_elem_all = np.genfromtxt(full_path,delimiter=' ',dtype='int', usecols=(0))
		points_ID_elem=points_ID_elem_all-number_elements_2D
		points_ID_elem=points_ID_elem.tolist()
		points_ID_elem_all=points_ID_elem_all.tolist()


#		Gauss points coordinates
		this_file_name=file_names.get_Gauss_points_coordinates_file_name()
		full_path=os.path.join(folder_name,this_file_name)
		coordinates = np.genfromtxt(full_path,delimiter=' ',dtype='double')


#		Fields
		this_file_name=file_names.get_Gauss_points_H_field_file_name()
#		this_file_name="H_source_FFEM.txt"

		full_path=os.path.join(folder_name,this_file_name)
		fields = np.genfromtxt(full_path,delimiter=' ',dtype='double')
		for elem_counter in range(0,number_elements):
			this_elem_type=elem_type_3D[elem_counter]
			gauss_points=get_gauss_points_class.get_gauss_points(this_elem_type)
			number_integ_points=len(get_gauss_points_class.get_gauss_points(this_elem_type))
			this_points_field=list()
			if elem_counter in points_ID_elem:

				this_elem=points_ID_elem.index(elem_counter)
				for k in points_IDs[this_elem].tolist():
					Hxy=np.zeros((3,1))
					Hxy[0,0]=fields[k,0]
					Hxy[1,0]=fields[k,1]
					Hxy[2,0]=fields[k,2]


					this_points_field.append(Hxy)

			else:
				for k in xrange(number_integ_points):
					Hxy=np.zeros((3,1))
					this_points_field.append(Hxy)
			field_solution.append(this_points_field)


	run_external_circuit=False
	if len(coupling)>0:
		run_external_circuit=True


#%%Creates the face list
	print_message("Creating faces list")
	for elem_counter in range(0,number_elements):
		number_local_faces=shape_functions.get_number_faces(this_elem_type)
		this_elem_type=elem_type_3D[elem_counter]
		this_element_nodes=elem_nodes_3D[elem_counter]
		faces_nodes_ID=shape_functions.get_nodes_ID_2_face(this_elem_type)
		number_faces,nodes_per_face=faces_nodes_ID.shape
		local_faces_ID=list()
		for local_face_counter in range(0,number_faces):
			nodes_list=list()
			for node_counter in range(nodes_per_face):
				node_ID=faces_nodes_ID[local_face_counter,node_counter]
				nodes_list.append(this_element_nodes[node_ID])
			local_faces_ID.append(face.add_to_list(nodes_list,elem_counter,faces_list))
		faces_ID.append(local_faces_ID)
	print_message("Creating faces list - Done")


#%%Integration
	print_message("Integration process")

	num_meshed_rel=len(faces_list)
	num_non_meshed_rel=len(external_reluctances)
	num_total_rel=num_meshed_rel+num_non_meshed_rel

#sparse matrix
	cols_rel_sparse=list()
	rows_rel_sparse=list()

	counter_elem_suf=0

#reluctance matrix
	diagonal=list()
	for each_element_faces in faces_ID:
		numbre_faces_this_element=len(each_element_faces)
		for face_counter_1 in xrange(numbre_faces_this_element):
			pos_1=each_element_faces[face_counter_1]
			for face_counter_2 in xrange(numbre_faces_this_element):
				pos_2=each_element_faces[face_counter_2]
				if pos_1==pos_2:
					if pos_1 not in diagonal:
						rows_rel_sparse.append(pos_1)
						cols_rel_sparse.append(pos_2)
						diagonal.append(pos_1)
				else:
					rows_rel_sparse.append(pos_1)
					cols_rel_sparse.append(pos_2)

	data_rel_sparse=np.zeros(len(rows_rel_sparse))
	faces_rel_spare=csr_matrix((data_rel_sparse, (rows_rel_sparse, cols_rel_sparse)), shape=(num_total_rel, num_total_rel))

#fmm matrix
	cols_fmm_sparse=np.zeros(num_meshed_rel)
	rows_fmm_sparse=xrange(0,num_meshed_rel)
	data_fmm_sparse=np.zeros(num_meshed_rel)
	fmm_sparse=csr_matrix((data_fmm_sparse, (rows_fmm_sparse, cols_fmm_sparse)), shape=(num_total_rel,1))

#source_flux matrix
	cols_source_flux_sparse=np.zeros(num_meshed_rel)
	rows_source_flux_sparse=xrange(0,num_meshed_rel)
	data_source_flux_sparse=np.zeros(num_meshed_rel)
	source_flux_sparse=csr_matrix((data_source_flux_sparse, (rows_source_flux_sparse, cols_source_flux_sparse)), shape=(num_total_rel,1))
#grad_phi matrix
#	cols_grad_phi_sparse=np.zeros(num_meshed_rel)
#	rows_grad_phi_sparse=xrange(0,num_meshed_rel)
#	data_grad_phi_sparse=np.zeros(num_meshed_rel)
#	grad_phi_sparse=csr_matrix((data_grad_phi_sparse, (rows_grad_phi_sparse, cols_grad_phi_sparse)), shape=(num_total_rel,1))

	this_elem_type=""
	for elem_counter in xrange(number_elements):
		this_elem_type_changed=elem_type_3D[elem_counter]
		if this_elem_type!=this_elem_type_changed:
			this_elem_type=this_elem_type_changed
			gauss_points=get_gauss_points_class.get_gauss_points(this_elem_type)
			number_local_faces=shape_functions.get_number_faces(this_elem_type)
			number_integ_points=len(get_gauss_points_class.get_gauss_points(this_elem_type))
			wtri=get_gauss_points_class.get_integration_weight(this_elem_type)

		faces_ID_Elem=faces_ID[elem_counter]
		this_element_nodes=elem_nodes_3D[elem_counter]
		mur_r=materials_lib[region_ID_list_3D[elem_counter]].Permeability
		mu_elem=vacuum.mu0*mur_r

		k_sf=1.0
		if run_VS:
			if mur_r>1.0:
				k_sf=-1.0*mu0*((1.0/mu_elem)-(1.0/mu0))
			else:
				k_sf=0


# Get W at reference element
		w_local_this_element=list() #[gauss point][face]
		for each_integ_point in xrange(number_integ_points):

#u,v,w coordinates
			u=gauss_points[each_integ_point,0]
			v=gauss_points[each_integ_point,1]
			w=gauss_points[each_integ_point,2]

# Shape functions @ reference element
			w_local_this_point=shape_functions.get_facet_shape_function(this_elem_type,u,v,w)
			w_local_this_element.append(w_local_this_point)

# Shape functions @ real element for each face
		w_real_all_points=list() # w_real_lista[0] contains  the shape function of all points for face 0

#   Face 0...Fn
#P0  W
#Pn

		for face_counter in xrange(number_local_faces):
			w_real_this_point=list()
			for point_counter in  range(0,number_integ_points):
				w_local=w_local_this_element[point_counter][face_counter]
				w_real=operations.convert_local_real_Piola(this_elem_type,w_local[0,0],w_local[0,1],w_local[0,2],this_element_nodes,nodes_coordenates)
				w_real_this_point.append(w_real)
			w_real_all_points.append(w_real_this_point)

# Source fields
		elem_ID_all=elem_counter+number_elements_2D
		for local_face_counter in xrange(number_local_faces):

			w_1=copy.deepcopy(w_real_all_points[local_face_counter])
			face_ID_1=faces_ID_Elem[local_face_counter]

			if faces_list[face_ID_1].elem_2==elem_counter:
				for each in w_1:
					each=matrix_aux.invert_w(each)

# mmf source integration process

#			if (52 in faces_list[face_ID_1].nodes_list) and (118 in faces_list[face_ID_1].nodes_list) and (384 in faces_list[face_ID_1].nodes_list):
#				faces_list[face_ID_1].print_face()
#				run_this_face=True


			counter_nodes=0
			for each in faces_list[face_ID_1].nodes_list:
				if  each in nodes_phys_surf:
					counter_nodes=counter_nodes+1
#					run_this_face=False
			run_this_face=False

			if  elem_counter in points_ID_elem:
				run_this_face=True


#			if (50 in faces_list[face_ID_1].nodes_list) and (120 in faces_list[face_ID_1].nodes_list):
#				run_this_face=True
#				faces_list[face_ID_1].print_face()
##					print(faces_list[face_ID_1].nodes_list)

			if run_this_face:

#Gets the ID of the element
				this_3D_ID=points_ID_elem_all.index(elem_ID_all)
#				print(this_3D_ID)
				this_face_nodes=faces_list[face_ID_1].nodes_list
#				faces_list[face_ID_1].print_face()


				source=0
				for each_integ_point in xrange(number_integ_points):

#					this_Gauss_point_ID=points_IDs[this_3D_ID][each_integ_point]

#					if run_biot_savart or run_permanent_magnets:
					Hxy=np.zeros((3,1))
					this_gauss_point_ID=points_IDs[this_3D_ID][each_integ_point]
					Hxy[0,0]=fields[this_gauss_point_ID][0]
					Hxy[1,0]=fields[this_gauss_point_ID][1]
					Hxy[2,0]=fields[this_gauss_point_ID][2]


#						Hxy=field_solution[elem_counter][each_integ_point]*k_sf

					w_1_this_point=w_1[each_integ_point]
#u,v,p coordinates
					u=gauss_points[each_integ_point,0]
					v=gauss_points[each_integ_point,1]
					p=gauss_points[each_integ_point,2]
					w=w_1_this_point

# Normal vector
					node1=this_face_nodes[0]
					node2=this_face_nodes[1]
					node3=this_face_nodes[2]
					P_1=np.array([nodes_coordenates[node1][0],nodes_coordenates[node1][1],nodes_coordenates[node1][2]])
					P_2=np.array([nodes_coordenates[node2][0],nodes_coordenates[node2][1],nodes_coordenates[node2][2]])
					P_3=np.array([nodes_coordenates[node3][0],nodes_coordenates[node3][1],nodes_coordenates[node3][2]])
					A=P_2-P_1
					B=P_3-P_1
					AxB=np.cross(A,B)
					nor=linalg.norm(AxB)
					n=AxB/nor
					n=np.array([[n[0]],[n[1]],[n[2]]])
#Shape funtions
					vdotn=matrix_aux.dot_product(w,n)
					w_n=n*vdotn
					w_t=w-w_n
					w=-w_n
					plot_shape_functions.append(w)
					plot_test_coord.append(coordinates[this_gauss_point_ID])
#Source field
					vdotn=matrix_aux.dot_product(Hxy,n)
					Hxy_n=n*vdotn
					plot_field.append(Hxy)
# Jacobian
					jac=operations.get_jacobian(this_elem_type,this_element_nodes,nodes_coordenates,u,v,p)
					det_jac=np.linalg.det(jac)
					abs_det_jac=np.abs(det_jac)
#Integration
					source=source+wtri*abs_det_jac*matrix_aux.dot_product(w,Hxy)

				fmm_sparse[face_ID_1,0]=fmm_sparse[face_ID_1,0]+source

# Relutances integration process
			for local_face_counter_2 in xrange(number_local_faces):
				w_2=copy.deepcopy(w_real_all_points[local_face_counter_2])
				face_ID_2=faces_ID_Elem[local_face_counter_2]

				if faces_list[face_ID_2].elem_2==elem_counter:
					 for each in w_2:
						 each=matrix_aux.invert_w(each)

				wtot=0.0
				for each_integ_point in range(0,number_integ_points):
					 u=gauss_points[each_integ_point,0]
					 v=gauss_points[each_integ_point,1]
					 p=gauss_points[each_integ_point,2]

# Jacobian
					 jac=operations.get_jacobian(this_elem_type,this_element_nodes,nodes_coordenates,u,v,p)
					 det_jac=np.linalg.det(jac)
					 abs_det_jac=np.abs(det_jac)

# Reluctance
					 w_1_this_point=w_1[each_integ_point]
					 w_2_this_point=w_2[each_integ_point]
					 wtot=wtot+wtri*abs_det_jac*matrix_aux.dot_product(w_1_this_point,w_2_this_point)/mu_elem

				faces_rel_spare[face_ID_1,face_ID_2]+=wtot
	print_message("Integration process - Done")


#%% Connection between the physical line with the circuit node
	print_message("External faces")

	for counter,each_face in enumerate(faces_list):
		if each_face.elem_2==str_noflux_face:
			for each_face_con in elem_2D_ID:
				nodes_face_shared=all_elem_nodes_3D[each_face_con]
				phys_line=elem_tags[each_face_con][0]

#Coupling with external reluctances
				for each_coupling in coupling:
					if each_coupling.PhysLine==phys_line:

						bool_connect=True
						for each_node_this_face in each_face.nodes_list:
							if each_node_this_face not in nodes_face_shared:
								bool_connect=False

						if bool_connect:
# Redefine the face
							   new_face=Face(each_face.nodes_list,each_face.elem_1,each_coupling.Node+number_elements)
							   faces_list[counter]=new_face
							   each_coupling.Face_ID_List.append(counter)

#%% Insert the flux sources

	BC_nodes=list()
	if run_surface_integral:
		folder_name=os.path.join(folder_path,results_folder)
		full_path=os.path.join(folder_name,"flux_surface.txt")
		flux_data = np.genfromtxt(full_path,delimiter=' ',dtype='double')
		flux_source =flux_data[:,1]
		flux_source_elem_ID=flux_data[:,0]
		num_faces_surface_integral=len(flux_source_elem_ID)
#		external_node_surface_ID_counter=0

		for face_counter in xrange(num_faces_surface_integral):
			this_elem_face_ID=int(flux_source_elem_ID[face_counter])
			this_face_nodes_elem=set(all_elem_nodes_3D[this_elem_face_ID])

			for counter,each_face in enumerate(faces_list):
				this_face_nodes=set(each_face.nodes_list)
				if this_face_nodes_elem.issubset(this_face_nodes):
#					print this_elem_face_ID
#					external_node_surface_ID=len(coupling)+number_elements-1
#					BC_nodes.append(external_node_surface_ID)
#					external_node_surface_ID_counter+=1
					new_face=Face(each_face.nodes_list,each_face.elem_1,each_face.elem_2)
					faces_list[counter]=new_face
					source_flux_sparse[counter]=flux_source[face_counter]
					faces_rel_spare[counter,counter]=10000000000000000.0
					fmm_sparse[counter,0]=0.0
#					print each_face.elem_1
#					break

	BC_values=[0]*len(BC_nodes)


#%% Delete the faces without external connections
	faces_ID_deleted_list=list()
	faces_deleted_list=list()

#Delete from reluctances and fmm matrix
	counter=0
	for face_counter in  xrange(len(faces_list)):
		if faces_list[face_counter].elem_2==str_noflux_face:
			faces_ID_deleted_list.append(face_counter)

	faces_rel_spare=matrix_aux.delete_sparse_mask(faces_rel_spare,faces_ID_deleted_list,0)
	faces_rel_spare=matrix_aux.delete_sparse_mask(faces_rel_spare,faces_ID_deleted_list,1)
	fmm_sparse=matrix_aux.delete_sparse_mask(fmm_sparse,faces_ID_deleted_list,0)
	source_flux_sparse=matrix_aux.delete_sparse_mask(source_flux_sparse,faces_ID_deleted_list,0)

##Delete from faces_list
	counter=0
	for each in faces_ID_deleted_list:
		face_ID=each+counter
		this_face=faces_list[face_ID]
		faces_list.remove(this_face)
		faces_deleted_list.append(this_face)
		counter-=1

#%% Add the external circuit reluctances
	number_deleted=len(faces_deleted_list)
	for counter in xrange(num_non_meshed_rel):

#reluctance value
		material=external_reluctances[counter].Material
		mur=materials_lib[material].Permeability
		LS=external_reluctances[counter].LS
		mu_elem=vacuum.mu0*mur
		reluctance_value=LS/mu_elem

		this_position=num_meshed_rel-number_deleted+counter
		faces_rel_spare[this_position,this_position]=reluctance_value
		fmm_sparse[this_position]=external_reluctances[counter].fmm
		source_flux_sparse[this_position]=external_reluctances[counter].flux


	external_nodes_list=list()

	for each in external_reluctances:

#Get the list of external nodes
		if each.node_from not in external_nodes_list:
			external_nodes_list.append(each.node_from)
		if each.node_to not in external_nodes_list:
			external_nodes_list.append(each.node_to)

#create a new face in the faces_list
		new_face=Face([],each.node_from+number_elements,each.node_to+number_elements)
		faces_list.append(new_face)

#Get the list of external nodes
	for each in coupling:
		if each.Node not in external_nodes_list:
			external_nodes_list.append(each.Node )

	print_message("External faces - Done")


#%% Incidence matrix
	print_message("Incidence matrix")
	external_nodes=0

	if run_external_circuit:
		external_nodes+=len(external_nodes_list)
#	elif run_surface_integral:
#		external_nodes+=len(BC_nodes)
	else:
		external_nodes+=0

	number_faces_list=len(faces_list)
	total_nodes=number_elements+external_nodes

	rows_incidence_sparse=list()
	cols_incidence_sparse=list()
	data_incidence_sparse=list()

	for counter in xrange(number_faces_list):
		this_face=faces_list[counter]
		rows_incidence_sparse.append(this_face.elem_1)
		cols_incidence_sparse.append(counter)
		data_incidence_sparse.append(1.0)

		rows_incidence_sparse.append(this_face.elem_2)
		cols_incidence_sparse.append(counter)
		data_incidence_sparse.append(-1.0)

	incidence_matrix_sparse=csr_matrix((data_incidence_sparse, (rows_incidence_sparse, cols_incidence_sparse)), shape=(total_nodes,number_faces_list))
	print_message("Incidence matrix - Done")


#%%Plot test fields
	Gmsh_file_name="test_H_field.txt"
	path=os.path.join(results_path,Gmsh_file_name)
	Create_Vector_field(plot_test_coord,plot_field,path,"H test")

	Gmsh_file_name="test_W.txt"
	path=os.path.join(results_path,Gmsh_file_name)
	Create_Vector_field(plot_test_coord,plot_shape_functions,path,"Shape function")

	return faces_rel_spare,incidence_matrix_sparse,fmm_sparse,source_flux_sparse,faces_ID,results_path,faces_ID_deleted_list,faces_list,faces_deleted_list,BC_nodes,BC_values
def integration_process(folder_path, preProcData):
    file_names = File_names()
    results_folder = file_names.get_results_folder_name()
    results_path = os.path.join(folder_path, results_folder)

    #%% Instances and geral definitions
    aux_RNM = AuxMethodsRNM()
    global_variables = GlobalVariables()
    error = Errors()
    operations = Operations()
    materials_lib = get_materials_lib()
    vacuum = Vacuum()
    get_gauss_points_class = GaussPoints()
    shape_functions = ShapeFuncions()
    operations = Operations()

    str_noflux_face = global_variables.str_noflux_face
    open_circuit_reluctance = global_variables.magnetic_open_circuit_reluctance
    results_folder = file_names.get_results_folder_name()

    face = Face()
    # ------------------------------------------------------------------------------
    # Setup
    regions_material = preProcData.RegionMaterial
    regions_excitation = preProcData.RegionExcitation
    boundary = preProcData.BC
    external_reluctances = preProcData.ExternalReluctances
    coupling = preProcData.CoupNet
    # ------------------------------------------------------------------------------
    # Mesh
    mesh_data = preProcData.MeshData
    all_elem_nodes_3D = mesh_data.ElemNodes
    nodes_coordenates = mesh_data.NodesCoordenates
    elem_tags = mesh_data.ElemTags
    elem_type = mesh_data.ElemType

    #%%Get source field

    # Run Biot-Savart
    run_biot_savart = False
    # 	for eachregion in regions_excitation:
    # 		 if eachregion.Value != 0.0:
    # 			 field_solution=Biot_Savart.run_Biot_Savart(setup_file_name,mesh_file_name,folder_path)
    # 		 run_biot_savart=True
    # 		 break

    # Run Permanent Magnets
    run_permanent_magnets = False
    for each_region in regions_material:
        for each in materials_lib[each_region.MaterialName].Hc:
            if each != 0.0:
                field_solution = permanent_magnets.run_permanent_magnets(preProcData, folder_path)
                run_permanent_magnets = True
                break

                # Read the file
    if run_biot_savart or run_permanent_magnets:
        (H_field, H_field_elem_nodes_3D) = get_Field_solution(
            os.path.join(results_path, file_names.get_H_results_file_name())
        )

    run_external_circuit = False
    if len(coupling) > 0:
        run_external_circuit = True

        #%% Get 2D and 3D elements, with their materials name
    elem_2D_ID = list()
    elem_type_3D = list()
    elem_nodes_3D = list()
    elem_tags_3D = list()
    region_ID_list_3D = list()
    number_elements_2D = 0

    for counter, each_elem in enumerate(all_elem_nodes_3D):
        this_elem_type = elem_type[counter]
        if this_elem_type < 4:
            elem_2D_ID.append(counter)
            number_elements_2D += 1
        else:
            elem_nodes_3D.append(each_elem)
            elem_type_3D.append(elem_type[counter])
            elem_tags_3D.append(elem_tags[counter])

            find = False
            for each_region in regions_material:
                if each_region.RegionNumber == elem_tags[counter][0]:
                    region_ID_list_3D.append(each_region.MaterialName)
                    find = True
            if not find:
                error.physical_surface_not_defined(str(each_region.RegionNumber), elem_tags[counter][0])

    number_elements = len(elem_nodes_3D)
    number_nodes = len(nodes_coordenates)
    faces_ID = list()
    faces_list = list()

    #%%Creates the face list
    print_message("Creating faces list")
    for elem_counter in range(0, number_elements):
        number_local_faces = shape_functions.get_number_faces(this_elem_type)
        this_elem_type = elem_type_3D[elem_counter]
        this_element_nodes = elem_nodes_3D[elem_counter]
        faces_nodes_ID = shape_functions.get_nodes_ID_2_face(this_elem_type)
        number_faces, nodes_per_face = faces_nodes_ID.shape
        local_faces_ID = list()
        for local_face_counter in range(0, number_faces):
            nodes_list = list()
            for node_counter in range(nodes_per_face):
                node_ID = faces_nodes_ID[local_face_counter, node_counter]
                nodes_list.append(this_element_nodes[node_ID])
            local_faces_ID.append(face.add_to_list(nodes_list, elem_counter, faces_list))
        faces_ID.append(local_faces_ID)
    print_message("Creating faces list - Done")

    #%%Integration
    print_message("Integration process")

    num_meshed_rel = len(faces_list)
    num_non_meshed_rel = len(external_reluctances)
    num_total_rel = num_meshed_rel + num_non_meshed_rel

    # sparse matrix
    cols_rel_sparse = list()
    rows_rel_sparse = list()

    # reluctance matrix
    diagonal = list()
    for each_element_faces in faces_ID:
        numbre_faces_this_element = len(each_element_faces)
        for face_counter_1 in xrange(numbre_faces_this_element):
            pos_1 = each_element_faces[face_counter_1]
            for face_counter_2 in xrange(numbre_faces_this_element):
                pos_2 = each_element_faces[face_counter_2]
                if pos_1 == pos_2:
                    if pos_1 not in diagonal:
                        rows_rel_sparse.append(pos_1)
                        cols_rel_sparse.append(pos_2)
                        diagonal.append(pos_1)
                else:
                    rows_rel_sparse.append(pos_1)
                    cols_rel_sparse.append(pos_2)

    data_rel_sparse = np.zeros(len(rows_rel_sparse))
    faces_rel_spare = csr_matrix(
        (data_rel_sparse, (rows_rel_sparse, cols_rel_sparse)), shape=(num_total_rel, num_total_rel)
    )
    # fmm matrix
    cols_fmm_sparse = np.zeros(num_meshed_rel)
    rows_fmm_sparse = xrange(0, num_meshed_rel)
    data_fmm_sparse = np.zeros(num_meshed_rel)
    fmm_sparse = csr_matrix((data_fmm_sparse, (rows_fmm_sparse, cols_fmm_sparse)), shape=(num_total_rel, 1))

    faces_rel_matrix = np.zeros((num_meshed_rel, num_meshed_rel))
    faces_fmm_matrix = np.zeros((num_meshed_rel, 1))
    xy_integ_points_list = list()
    W_integ_points_list = list()

    this_elem_type = ""
    for elem_counter in xrange(number_elements):
        this_elem_type_changed = elem_type_3D[elem_counter]
        if this_elem_type != this_elem_type_changed:
            this_elem_type = this_elem_type_changed
            gauss_points = get_gauss_points_class.get_gauss_points(this_elem_type)
            number_local_faces = shape_functions.get_number_faces(this_elem_type)
            number_integ_points = len(get_gauss_points_class.get_gauss_points(this_elem_type))
            wtri = get_gauss_points_class.get_integration_weight(this_elem_type)

        faces_ID_Elem = faces_ID[elem_counter]
        this_element_nodes = elem_nodes_3D[elem_counter]
        mu_elem = vacuum.mu0 * materials_lib[region_ID_list_3D[elem_counter]].Permeability

        # Get W at reference element
        w_local_this_element = list()  # [gauss point][face]
        for each_integ_point in xrange(number_integ_points):

            # u,v,w coordinates
            u = gauss_points[each_integ_point, 0]
            v = gauss_points[each_integ_point, 1]
            w = gauss_points[each_integ_point, 2]

            # Shape functions @ reference element
            w_local_this_point = shape_functions.get_facet_shape_function(this_elem_type, u, v, w)
            w_local_this_element.append(w_local_this_point)

        # Shape functions @ real element for each face
        w_real_all_points = list()  # w_real_lista[0] contains  the shape function of all points for face 0

        #   Face 0...Fn
        # P0  W
        # Pn

        for face_counter in xrange(number_local_faces):
            w_real_this_point = list()
            for point_counter in range(0, number_integ_points):
                w_local = w_local_this_element[point_counter][face_counter]
                w_real = operations.convert_local_real_Piola(
                    this_elem_type, w_local[0, 0], w_local[0, 1], w_local[0, 2], this_element_nodes, nodes_coordenates
                )
                w_real_this_point.append(w_real)
            w_real_all_points.append(w_real_this_point)

        # Source fields
        if run_biot_savart or run_permanent_magnets:
            H_points = H_field_elem_nodes_3D[elem_counter]

        for local_face_counter in xrange(number_local_faces):

            w_1 = copy.deepcopy(w_real_all_points[local_face_counter])
            face_ID_1 = faces_ID_Elem[local_face_counter]

            if faces_list[face_ID_1].elem_2 == elem_counter:
                for each in w_1:
                    each = matrix_aux.invert_w(each)

            # mmf source integration process
            source = 0
            for each_integ_point in xrange(number_integ_points):
                w_1_this_point = w_1[each_integ_point]

                u = gauss_points[each_integ_point, 0]
                v = gauss_points[each_integ_point, 1]
                p = gauss_points[each_integ_point, 2]
                w = w_1_this_point

                xy_coord = operations.convert_local_real(this_elem_type, u, v, p, this_element_nodes, nodes_coordenates)
                xy_integ_points_list.append(xy_coord)
                W_integ_points_list.append(w)

                if run_biot_savart or run_permanent_magnets:
                    H_point = H_points[each_integ_point]
                    Hx = H_field[H_point][0]
                    Hy = H_field[H_point][1]
                    Hz = H_field[H_point][2]

                    if (Hx != 0) or (Hy != 0) or (Hz != 0):
                        Hxy = np.array([[Hx], [Hy], [Hz]])

                        # Jacobian
                        jac = operations.get_jacobian(this_elem_type, this_element_nodes, nodes_coordenates, u, v)
                        det_jac = np.linalg.det(jac)
                        abs_det_jac = np.abs(det_jac)

                        source = source + wtri * abs_det_jac * aux_RNM.dot_product(w, Hxy)

            aux_RNM.fmm_matrix_control(face_ID_1, faces_fmm_matrix, source, False, faces_list, str_noflux_face)
            fmm_sparse[face_ID_1] += source

            # Relutances integration process
            for local_face_counter_2 in xrange(number_local_faces):
                w_2 = copy.deepcopy(w_real_all_points[local_face_counter_2])
                face_ID_2 = faces_ID_Elem[local_face_counter_2]

                if faces_list[face_ID_2].elem_2 == elem_counter:
                    for each in w_2:
                        each = matrix_aux.invert_w(each)

                wtot = 0.0
                for each_integ_point in range(0, number_integ_points):
                    u = gauss_points[each_integ_point, 0]
                    v = gauss_points[each_integ_point, 1]
                    p = gauss_points[each_integ_point, 2]

                    # Jacobian
                    jac = operations.get_jacobian(this_elem_type, this_element_nodes, nodes_coordenates, u, v, p)
                    det_jac = np.linalg.det(jac)
                    abs_det_jac = np.abs(det_jac)

                    # Reluctance
                    w_1_this_point = w_1[each_integ_point]
                    w_2_this_point = w_2[each_integ_point]
                    wtot = wtot + wtri * abs_det_jac * matrix_aux.dot_product(w_1_this_point, w_2_this_point) / mu_elem

                aux_RNM.reluctance_matrix_control(
                    face_ID_1, face_ID_2, faces_rel_matrix, wtot, False, faces_list, str_noflux_face
                )
                faces_rel_spare[face_ID_1, face_ID_2] += wtot
    print_message("Integration process - Done")

    # Connection between the physical line with the circuit node
    print_message("External faces")
    magnetic_short_circuit_reluctance = global_variables.magnetic_short_circuit_reluctance

    for counter, each_face in enumerate(faces_list):
        if each_face.elem_2 == str_noflux_face:
            for each_face_con in elem_2D_ID:
                nodes_face_shared = all_elem_nodes_3D[each_face_con]
                phys_line = elem_tags[each_face_con][0]

                for each_coupling in coupling:
                    if each_coupling.PhysLine == phys_line:

                        bool_connect = True
                        for each_node_this_face in each_face.nodes_list:
                            if each_node_this_face not in nodes_face_shared:
                                bool_connect = False

                        if bool_connect:
                            # Redefine the face
                            new_face = Face(
                                each_face.nodes_list, each_face.elem_1, each_coupling.Node + number_elements
                            )
                            faces_list[counter] = new_face
                            each_coupling.Face_ID_List.append(counter)

    # Set the reluctance as a magnetic short circuit
    # 							   aux_RNM.reluctance_matrix_control(counter,counter,faces_rel_spare,magnetic_short_circuit_reluctance,False)

    #%% Delete the faces without external connections
    faces_ID_deleted_list = list()
    faces_deleted_list = list()

    # Delete from reluctances and fmm matrix
    counter = 0
    for face_counter in xrange(len(faces_list)):
        if faces_list[face_counter].elem_2 == str_noflux_face:
            faces_ID_deleted_list.append(face_counter)

    faces_rel_matrix = np.delete(faces_rel_matrix, faces_ID_deleted_list, axis=0)
    faces_rel_matrix = np.delete(faces_rel_matrix, faces_ID_deleted_list, axis=1)
    faces_fmm_matrix = np.delete(faces_fmm_matrix, faces_ID_deleted_list, axis=0)

    faces_rel_spare = matrix_aux.delete_sparse_mask(faces_rel_spare, faces_ID_deleted_list, 0)
    faces_rel_spare = matrix_aux.delete_sparse_mask(faces_rel_spare, faces_ID_deleted_list, 1)
    fmm_sparse = matrix_aux.delete_sparse_mask(fmm_sparse, faces_ID_deleted_list, 0)

    ##Delete from faces_list
    counter = 0
    for each in faces_ID_deleted_list:
        face_ID = each + counter
        this_face = faces_list[face_ID]
        faces_list.remove(this_face)
        faces_deleted_list.append(this_face)
        counter -= 1

    #%% Add the external circuit reluctances
    number_deleted = len(faces_deleted_list)
    for counter in xrange(num_non_meshed_rel):

        # reluctance value
        material = external_reluctances[counter].Material
        mur = materials_lib[material].Permeability
        LS = external_reluctances[counter].LS
        mu_elem = vacuum.mu0 * mur
        reluctance_value = LS / mu_elem

        this_position = num_meshed_rel - number_deleted + counter
        faces_rel_spare[this_position, this_position] = reluctance_value
        fmm_sparse[this_position] = external_reluctances[counter].fmm

    external_nodes_list = list()
    rows, cols = faces_rel_matrix.shape
    for each in external_reluctances:

        mu_elem = vacuum.mu0 * materials_lib[each.Material].Permeability

        # Get the list of external nodes
        if each.node_from not in external_nodes_list:
            external_nodes_list.append(each.node_from)
        if each.node_to not in external_nodes_list:
            external_nodes_list.append(each.node_to)

        # add the reluctance in the matrix system
        row_matrix = np.zeros((1, cols))
        faces_rel_matrix = np.vstack((faces_rel_matrix, row_matrix))
        rows += 1
        col_matrix = np.zeros((rows, 1))
        faces_rel_matrix = np.hstack((faces_rel_matrix, col_matrix))
        cols += 1
        faces_fmm_matrix = np.vstack((faces_fmm_matrix, each.fmm))

        # reluctance value
        reluctance_value = each.LS / mu_elem
        faces_rel_matrix[rows - 1, cols - 1] = reluctance_value

        # create a new face in the faces_list
        new_face = Face([], each.node_from + number_elements, each.node_to + number_elements)
        faces_list.append(new_face)

    # Get the list of external nodes
    for each in coupling:
        if each.Node not in external_nodes_list:
            external_nodes_list.append(each.Node)

    print_message("External faces - Done")

    #%% Incidence matrix
    print_message("Incidence matrix")
    external_nodes = 0

    if run_external_circuit:
        external_nodes += len(external_nodes_list)
    else:
        external_nodes += 0

    number_faces_list = len(faces_list)
    total_nodes = number_elements + external_nodes
    incidence_matrix = np.zeros((total_nodes, number_faces_list))

    rows_incidence_sparse = list()
    cols_incidence_sparse = list()
    data_incidence_sparse = list()

    for counter in xrange(number_faces_list):
        this_face = faces_list[counter]
        rows_incidence_sparse.append(this_face.elem_1)
        cols_incidence_sparse.append(counter)
        data_incidence_sparse.append(1.0)

        rows_incidence_sparse.append(this_face.elem_2)
        cols_incidence_sparse.append(counter)
        data_incidence_sparse.append(-1.0)

    incidence_matrix_sparse = csr_matrix(
        (data_incidence_sparse, (rows_incidence_sparse, cols_incidence_sparse)), shape=(total_nodes, number_faces_list)
    )

    for counter, each_face in enumerate(faces_list):
        if each_face.elem_2 != str_noflux_face:
            incidence_matrix[each_face.elem_1, counter] = 1
            incidence_matrix[each_face.elem_2, counter] = -1
        else:
            incidence_matrix[each_face.elem_1, counter] = 1
            incidence_matrix[total_nodes - 1, counter] = -1

    print_message("Incidence matrix - Done")

    return (
        faces_rel_spare,
        incidence_matrix_sparse,
        fmm_sparse,
        faces_ID,
        results_path,
        faces_rel_matrix,
        incidence_matrix,
        faces_fmm_matrix,
        faces_ID_deleted_list,
        faces_list,
        faces_deleted_list,
    )